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The goal of this monograph is to develop a mathematical theory of open fluid systems in the framework of continuum thermodynamics. Part I discusses the difference between open and closed fluid systems and introduces the Navier-Stokes-Fourier system as the mathematical model of a fluid in motion that will be used throughout the text. A class of generalized solutions to the Navier-Stokes-Fourier system is considered in Part II in order to show existence of global-in-time solutions for any finite energy initial data, as well as to establish the weak-strong uniqueness principle.  Finally,...

Many problems in mathematical fluid dynamics involve the behavior of solutions of nonlinear systems of partial differential equations. This book is an introduction to the problems involving singular limits based on the concept of weak or variational solutions.

This book provides a comprehensive introduction to the mathematical theory of compressible flow, describing both inviscid and viscous compressible flow, which are governed by the Euler and Navier-Stokes equations respectively. The method of presentation allows readers with different backgrounds to focus on various modules of the material, either in part or more fully. Chapters include detailed heuristic arguments providing motivation for technical details that are rigorously presented later on in the text. This especially concerns the existence theory for steady and unsteady Navier-Stokes...